Trigonometry and Complex Numbers Assignment

<p>45° (D)</p> Signup and view all the answers

<p>2 - i (C)</p> Signup and view all the answers

<p>1 (D)</p> Signup and view all the answers

<p>$\frac{-1}{2}$ (C)</p> Signup and view all the answers

<p>1 (A)</p> Signup and view all the answers

<p>-1 (B)</p> Signup and view all the answers

<p>√2/2 (A)</p> Signup and view all the answers

<p>(4 + 5i) (B)</p> Signup and view all the answers

<p>2 + 10i (A)</p> Signup and view all the answers

<p>-7 + 6i (B)</p> Signup and view all the answers

<p>6 - 2i (D)</p> Signup and view all the answers

The Sine function (sin x) takes an angle (x) as input and returns the y-coordinate of a point on the unit circle.

The Cosine function (cos x) takes an angle (x) as input and returns the x-coordinate of a point on the unit circle.

The Tangent function (tan x) is the ratio of the Sine function (sin x) to the Cosine function (cos x). It can be visualized as the slope of a line drawn from the origin to a point on the unit circle.

The Cotangent function (cot x) is the reciprocal of the Tangent function (tan x). It is also the ratio of the Cosine function (cos x) to the Sine function (sin x).

The Secant function (sec x) is the reciprocal of the Cosine function (cos x). It represents the length of the line segment from the origin to a point on the unit circle.

The Cosecant function (csc x) is the reciprocal of the Sine function (sin x). It represents the length of the line segment from the origin to a point on the unit circle.

Complex numbers consist of a real part and an imaginary part. They are expressed in the form a + bi, where 'a' and 'b' are real numbers and 'i' is the imaginary unit (√-1).

The conjugate of a complex number (a + bi) is obtained by changing the sign of the imaginary part. It is represented as a - bi.

The radian measure of 150 degrees is 5π/6.

The square of 4i is (4i)² = 16i² = 16(-1) = -16. Adding 8 gives -16 + 8 = -8.

An angle of 240 degrees lies in the third quadrant.

The reference angle of 135° is 45°.

Subtracting (1+2i) from (3+2i) gives (3+2i) - (1+2i) = (3-1) + (2-2)i = 2

The hypotenuse of a right triangle is the side opposite the right angle. Here, the hypotenuse is 10m (using the Pythagorean theorem: 6² + 8² = 10² ).

i¹⁶ is found by cycling through powers of i: i¹, i², i³, i⁴, and noticing the pattern repeats. i¹⁶ is the same as (i⁴)⁴ = 1⁴ = 1.

The sine of a negative angle is the negative of the sine of the corresponding positive angle. sin(-30°) = - sin(30°) = -1/2.